Dynamical law of the phase interface motion in the presence of crystals nucleation

Abstract

In this paper, we develop a theory of solid/liquid phase interface motion into an undercooled melt in the presence of nucleation and growth of crystals. A set of integrodifferential kinetic, heat and mass transfer equations is analytically solved in the two-phase and liquid layers divided by the moving phase transition interface. To do this, we have used the saddle-point method to evaluate a Laplace-type integral and the small parameter method to find the law of phase interface motion. The main result is that the phase interface Z propagates into an undercooled melt with time t as Z(t)=σt+εχt7/2 with allowance for crystal nucleation. The effect of nucleation is in the second contribution, which is proportional to t7 / 2 whereas the first term ∼t represents the well-known self-similar solution. The nucleation and crystal growth processes are responsible for the emission of latent crystallization heat, which reduces the melt undercooling and constricts the two-phase layer thickness (parameter χ< 0). © 2022, The Author(s).